I usually start with anime on cartoon network/adult swim, then start reading the manga afterwards. Usually because I want to know what happens next without waiting another week for a new episode.
The only exception is Death Note. I read the manga first, then watched the movies, then I'm gonna start watching the anime tonight when it airs on adult swim.
I normally read the manga first, since its the real thing. And it being the original, sometimes in the anime theres things that are left out or just loads of filler eps. Not saying that anime is bad or anything, its just as good.
I dont watch or read that much anime/manga anymore though.